A hardwired connection is more reliable than a wireless connection. The ideal setup to obtain a hardwired connection is to run a CAT5e/CAT6 out of the main router and into the room you're working in. From there, get an un-managed switch and this will allow you to connect your VoIP phone and work computer.
As for the existing Ethernet port in the room, you'd have to speak to someone who's has knowledge on how that was installed or you can run a cable trace test. But, I don't know where the other end would be so you may have to physically trace that wire (break down the wall and see where it goes), or just keep cable tracing every available Ethernet port.